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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
51.2.a.a	$51$	$2$	51.a	1.a	$1$	$1$	$1$	$0.407$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
51.2.a.b	$51$	$2$	51.a	1.a	$1$	$2$	$2$	$0.407$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(3\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)

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